Monotone linear transformations on matrices are invertible

Anna A. Alieva; Alexander E. Guterman

doi:10.1081/agb-200058398

Monotone linear transformations on matrices are invertible

Anna A. Alieva, Alexander E. Guterman

Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We show that monotone linear transformations on matrices with respect to <̄, <*, * <, < *, <, < ^σ, <^σ1-partial orders are invertible and provide a complete characterization of such transformations.

Original language	English
Pages (from-to)	3335-3352
Number of pages	18
Journal	Communications in Algebra
Volume	33
Issue number	9
DOIs	https://doi.org/10.1081/agb-200058398
State	Published - 1 Aug 2005
Externally published	Yes

Bibliographical note

Funding Information:
This work is partially supported by RFBR, grants YSF 03-55-1919 and NSH-1910.2003.01.

Funding

This work is partially supported by RFBR, grants YSF 03-55-1919 and NSH-1910.2003.01.

Funders	Funder number
Russian Foundation for Basic Research	NSH-1910.2003.01, YSF 03-55-1919

Keywords

Linear preservers
Matrix partial orders
Monotone transformations

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10.1081/agb-200058398

Cite this

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title = "Monotone linear transformations on matrices are invertible",

abstract = "We show that monotone linear transformations on matrices with respect to {\=<}, <*, * <, < *, <, < σ, <σ1-partial orders are invertible and provide a complete characterization of such transformations.",

keywords = "Linear preservers, Matrix partial orders, Monotone transformations",

author = "Alieva, {Anna A.} and Guterman, {Alexander E.}",

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AU - Guterman, Alexander E.

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N2 - We show that monotone linear transformations on matrices with respect to <̄, <*, * <, < *, <, < σ, <σ1-partial orders are invertible and provide a complete characterization of such transformations.

AB - We show that monotone linear transformations on matrices with respect to <̄, <*, * <, < *, <, < σ, <σ1-partial orders are invertible and provide a complete characterization of such transformations.

KW - Linear preservers

KW - Matrix partial orders

KW - Monotone transformations

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Monotone linear transformations on matrices are invertible

Abstract

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Keywords

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